Theoretical approaches are being developed to extract information concerning the nature of internal motions in a variety of biopolymers from nuclear magnetic relaxation and time-resolved fluorescence depolarization experiments. In order to interpret fluorescence studies where the time dependence of the anisotropy depends on excitation frequency and/or the total intensity is multiexponential, a comprehensive formalism has been developed that treats both excited state and orientation dynamics in a unified way. This approach readily handles not only overall and internal reorientation of probes but also such complications as energy transfer, heterogeneity and the interconversion of excited states with different emission characteristics. The role of diffusion in reaction dynamics and electrochemical processes has been investigated. A new approach has been developed to treat localized traps in diffusion processes and has been used to establish the relationship between the time-dependent germinate recombination yield and the bimolecular rate in diffusion influenced reactions. Novel Monte Carlo Brownian dynamics and finite difference algorithms have been developed and applied to the solution of realistic diffusion problems including the simulation of the current to microelectrodes that are used in vivo studies of the concentration of electroactive molecules.